Projects per year
Abstract
We prove that the complete graph with a hole Ku+w − Ku can be decomposed into cycles of arbitrary specified lengths provided that the obvious necessary conditions are satisfied, each cycle has length at most min(u, w), and the longest cycle is at most three times as long as the second longest. This generalises existing results on decomposing the complete graph with a hole into cycles of uniform length, and complements work on decomposing complete graphs, complete multigraphs, and complete multipartite graphs into cycles of arbitrary specified lengths.
Original language | English |
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Pages (from-to) | 1818-1843 |
Number of pages | 26 |
Journal | Discrete Mathematics |
Volume | 340 |
Issue number | 8 |
DOIs | |
Publication status | Published - 1 Aug 2017 |
Keywords
- Complete graph with a hole
- Cycle decomposition
- Graph decomposition
Projects
- 2 Finished
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Matchings in Combinatorial Structures
Wanless, I., Bryant, D. & Horsley, D.
Australian Research Council (ARC), Monash University, University of Queensland , University of Melbourne
1/01/15 → 10/10/20
Project: Research
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Partitioning and ordering Steiner triple systems
Australian Research Council (ARC)
1/03/12 → 31/12/17
Project: Research